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A119423 Denominators of coefficients in a continued fraction expansion of the Gamma function. 2

%I #7 Nov 11 2010 07:34:06

%S 2021,125896643,4596084813365743279,

%T 20539143739435534417826656817767471,

%U 154187684682287395130815676867766056654304274786409523983,53758055914442388300525602657237655353613236528990789014340068307611233396794963869,582235181033697130010052826698193975503732624065579606751772525345364278965643722001124189437614592415486167547436141091

%N Denominators of coefficients in a continued fraction expansion of the Gamma function.

%H David W. Cantrell, <a href="/A119423/b119423.txt">Table of n, a(n) for n = 1..18</a>

%H David W. Cantrell, <a href="http://groups.google.com/group/sci.math.num-analysis/msg/521fa1a6fb98a300">A new convergent expansion for the gamma function</a>, sci.math.num-analysis, Nov 05, 2001

%e For Re(z) > 0, Gamma(z + 1/2) = sqrt(2*pi)*(z/e)^z / [1 + 1/( 24*z - 1/2 + CF(z) )] where continued fraction CF(z) = 1/(c_1*z + 1/(c_2*z + 1/(c_3*z + ...))) with c_1 = 1440/2021, c_2 = 686186088/125896643, c_3 = 1521596612992267104/4596084813365743279, ...

%t See A119422.

%Y Numerators given in A119422.

%K frac,nonn

%O 1,1

%A David W. Cantrell (DWCantrell(AT)sigmaxi.net), May 18 2006

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